
[1]}
Assume \((V,\in _{\Delta _0})\)  models \(T_0\) . Then every projective subset of \(2^\omega \)  is universally Baire.

[1]}
Assume \((V,\in _{\Delta _0})\models T_1\) .
Then \(\mathsf {UB}\)  is projectively closed.

(Woodin, Unpublished)
Assume \((V,\in _{\Delta _0})\models T_2\) . Then the family of subsets of \(2^\omega \) 
which are definable by in \(L(\text{{\sf UB}})\)  consists of universally Baire sets.


